Speeding up Huff Form of Elliptic Curves.
Neriman Gamze Orhon, Hüseyin Hışıl · IACR Cryptology ePrint Archive · 2017
This paper presents faster inversion-free point addition formulas for the curve $$y (1+ax^2) = cx (1+dy^2)$$ . The proposed formulas improve the point doubling operation count record (I, M, S, D, a are arithmetic operations over a field. I: inversion, M: multiplication, S: squaring, D: multiplication by a curve constant, a: addition/subtraction) from $$6\mathbf{{M}}+ 5\mathbf{{S}}$$ to $$8\mathbf{{M}}$$ and mixed addition operation count record from $$10\mathbf{{M}}$$ to $$8\mathbf{{M}}$$ . Both sets of formulas are shown to be 4-way parallel, leading to an effective cost of $$2\mathbf{{M}}$$ per either of the group operations.